Polymorphic Uncertainty Modeling for Optimization of Timber Structures

Abstract

AbstractThe uncertainty characteristics of wood are mainly affected by natural variation. Out of this, the traditional approach of stochastic variables can be expanded to a polymorphic uncertainty model. Therefore, e.g. fuzzy probability based randomness is used by extending stochastic variables with fuzzy variables in parameterization concerning the distribution functions, see [1] and [2]. The coupling of both aleatoric and epistemic uncertainty is involved in the uncertainty analysis.The FEM is applied as basic solution of particular load situations on the focused timber structure. A local orthotropic formulation is used and the properties are evaluated on each integration point with respect to the tree trunk axis.In this contribution, an approach to polymorphic uncertainty modeling for timber structures is introduced. According to [3], models representing the spatial variation and interdependencies of material parameters are necessary for a realistic representation in numerical simulation. For this purpose, on the one hand interactions between fuzzy variables, on the other hand correlations among random variables are considered. Random fields are utilized to capture spatially varying material properties in context with the discretization of FE. Approaches to both spatially and structurally depending autocorrelations along with crosscorrelations based on [4] are presented.The preliminary steps aim at an optimization in design of timber structures, provided that polymorphic uncertain design as well as a priori parameters are considered. The developed tools for uncertainty analysis and the basic FEM solution are prepared as a basis for an automated optimization processing, whereas they are preferably parallelized, incorporating methods for reducing the numerical effort. Results of the uncertainty analysis of a timber structure are shown exemplary.